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GHA1 num und ana richtig. Tests nach Beispielen aus Panou 2013

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Hendrik Möllersmann
2025-12-10 11:45:41 +01:00
parent 936b7c56f9
commit 946d028fae
6 changed files with 335 additions and 102 deletions
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GHA_triaxial/panou.py
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@@ -1,4 +1,5 @@
import numpy as np
from numpy import sin, cos, sqrt, arctan2
import ellipsoide
import Numerische_Integration.num_int_runge_kutta as rk
import winkelumrechnungen as wu
@@ -6,33 +7,66 @@ import ausgaben as aus
import GHA.rk as ghark
from scipy.special import factorial as fact
from math import comb
import GHA_triaxial.numeric_examples_panou as nep
# Panou, Korakitits 2019
def gha1_num(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, num):
def gha1_num_old(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, num):
phi, lamb, h = ell.cart2geod("ligas3", point)
x, y, z = ell.geod2cart(phi, lamb, 0)
values = ell.p_q(x, y, z)
H = values["H"]
p = values["p"]
q = values["q"]
p, q = ell.p_q(x, y, z)
dxds0 = p[0] * np.sin(alpha0) + q[0] * np.cos(alpha0)
dyds0 = p[1] * np.sin(alpha0) + q[1] * np.cos(alpha0)
dzds0 = p[2] * np.sin(alpha0) + q[2] * np.cos(alpha0)
dxds0 = p[0] * sin(alpha0) + q[0] * cos(alpha0)
dyds0 = p[1] * sin(alpha0) + q[1] * cos(alpha0)
dzds0 = p[2] * sin(alpha0) + q[2] * cos(alpha0)
h = lambda dxds, dyds, dzds: dxds**2 + 1/(1-ell.ee**2)*dyds**2 + 1/(1-ell.ex**2)*dzds**2
f1 = lambda s, x, dxds, y, dyds, z, dzds: dxds
f2 = lambda s, x, dxds, y, dyds, z, dzds: -h(dxds, dyds, dzds) / H * x
f3 = lambda s, x, dxds, y, dyds, z, dzds: dyds
f4 = lambda s, x, dxds, y, dyds, z, dzds: -h(dxds, dyds, dzds) / H * y/(1-ell.ee**2)
f5 = lambda s, x, dxds, y, dyds, z, dzds: dzds
f6 = lambda s, x, dxds, y, dyds, z, dzds: -h(dxds, dyds, dzds) / H * z/(1-ell.ex**2)
f1 = lambda x, dxds, y, dyds, z, dzds: dxds
f2 = lambda x, dxds, y, dyds, z, dzds: -h(dxds, dyds, dzds) / ell.func_H(x, y, z) * x
f3 = lambda x, dxds, y, dyds, z, dzds: dyds
f4 = lambda x, dxds, y, dyds, z, dzds: -h(dxds, dyds, dzds) / ell.func_H(x, y, z) * y/(1-ell.ee**2)
f5 = lambda x, dxds, y, dyds, z, dzds: dzds
f6 = lambda x, dxds, y, dyds, z, dzds: -h(dxds, dyds, dzds) / ell.func_H(x, y, z) * z/(1-ell.ex**2)
funktionswerte = rk.verfahren([f1, f2, f3, f4, f5, f6], [x, dxds0, y, dyds0, z, dzds0], s, num, fein=False)
P2 = funktionswerte[-1]
P2 = (P2[0], P2[2], P2[4])
return P2
def buildODE(ell):
def ODE(v):
x, dxds, y, dyds, z, dzds = v
H = ell.func_H(x, y, z)
h = dxds**2 + 1/(1-ell.ee**2)*dyds**2 + 1/(1-ell.ex**2)*dzds**2
ddx = -(h/H)*x
ddy = -(h/H)*y/(1-ell.ee**2)
ddz = -(h/H)*z/(1-ell.ex**2)
return [dxds, ddx, dyds, ddy, dzds, ddz]
return ODE
def gha1_num(ell, point, alpha0, s, num):
phi, lam, _ = ell.cart2geod("ligas3", point)
x0, y0, z0 = ell.geod2cart(phi, lam, 0)
p, q = ell.p_q(x0, y0, z0)
dxds0 = p[0] * sin(alpha0) + q[0] * cos(alpha0)
dyds0 = p[1] * sin(alpha0) + q[1] * cos(alpha0)
dzds0 = p[2] * sin(alpha0) + q[2] * cos(alpha0)
v_init = [x0, dxds0, y0, dyds0, z0, dzds0]
F = buildODE(ell)
werte = rk.rk_chat(F, v_init, s, num)
x1, _, y1, _, z1, _ = werte[-1]
return x1, y1, z1
funktionswerte = rk.verfahren([f1, f2, f3, f4, f5, f6], [0, x, dxds0, y, dyds0, z, dzds0], s, num)
return funktionswerte
def checkLiouville(ell: ellipsoide.EllipsoidTriaxial, points):
constantValues = []
@@ -52,9 +86,9 @@ def checkLiouville(ell: ellipsoide.EllipsoidTriaxial, points):
P = p[0]*dxds + p[1]*dyds + p[2]*dzds
Q = q[0]*dxds + q[1]*dyds + q[2]*dzds
alpha = np.arctan(P/Q)
alpha = arctan2(P, Q)
c = ell.ay**2 - (t1 * np.sin(alpha)**2 + t2 * np.cos(alpha)**2)
c = ell.ay**2 - (t1 * sin(alpha)**2 + t2 * cos(alpha)**2)
constantValues.append(c)
pass
@@ -63,9 +97,7 @@ def gha1_ana(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, maxM):
"""
Panou, Korakitits 2020, 5ff.
:param ell:
:param x:
:param y:
:param z:
:param point:
:param alpha0:
:param s:
:param maxM:
@@ -77,21 +109,22 @@ def gha1_ana(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, maxM):
z_m = [z]
# erste Ableitungen (7-8)
sqrtH = np.sqrt(ell.p_q(x, y, z)["H"])
H = x ** 2 + y ** 2 / (1 - ell.ee ** 2) ** 2 + z ** 2 / (1 - ell.ex ** 2) ** 2
sqrtH = sqrt(H)
n = np.array([x / sqrtH,
y / ((1-ell.ee**2) * sqrtH),
z / ((1-ell.ex**2) * sqrtH)])
u, v = ell.cart2para(np.array([x, y, z]))
G = np.sqrt(1 - ell.ex**2 * np.cos(u)**2 - ell.ee**2 * np.sin(u)**2 * np.sin(v)**2)
q = np.array([-1/G * np.sin(u) * np.cos(v),
-1/G * np.sqrt(1-ell.ee**2) * np.sin(u) * np.sin(v),
1/G * np.sqrt(1-ell.ex**2) * np.cos(u)])
G = sqrt(1 - ell.ex**2 * cos(u)**2 - ell.ee**2 * sin(u)**2 * sin(v)**2)
q = np.array([-1/G * sin(u) * cos(v),
-1/G * sqrt(1-ell.ee**2) * sin(u) * sin(v),
1/G * sqrt(1-ell.ex**2) * cos(u)])
p = np.array([q[1]*n[2] - q[2]*n[1],
q[2]*n[0] - q[0]*n[2],
q[0]*n[1] - q[1]*n[0]])
x_m.append(p[0] * np.sin(alpha0) + q[0] * np.cos(alpha0))
y_m.append(p[1] * np.sin(alpha0) + q[1] * np.cos(alpha0))
z_m.append(p[2] * np.sin(alpha0) + q[2] * np.cos(alpha0))
x_m.append(p[0] * sin(alpha0) + q[0] * cos(alpha0))
y_m.append(p[1] * sin(alpha0) + q[1] * cos(alpha0))
z_m.append(p[2] * sin(alpha0) + q[2] * cos(alpha0))
# H Ableitungen (7)
H_ = lambda p: np.sum([comb(p, i) * (x_m[p - i] * x_m[i] +
@@ -143,32 +176,16 @@ def gha1_ana(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, maxM):
if __name__ == "__main__":
# ell = ellipsoide.EllipsoidTriaxial.init_name("Eitschberger1978")
ell = ellipsoide.EllipsoidTriaxial.init_name("BursaSima1980")
ellbi = ellipsoide.EllipsoidTriaxial.init_name("Bessel-biaxial")
ell = ellipsoide.EllipsoidTriaxial.init_name("BursaSima1980round")
# ellbi = ellipsoide.EllipsoidTriaxial.init_name("Bessel-biaxial")
re = ellipsoide.EllipsoidBiaxial.init_name("Bessel")
# Panou 2013, 7, Table 1, beta0=60°
beta1 = wu.deg2rad(60)
lamb1 = wu.deg2rad(0)
beta2 = wu.deg2rad(60)
lamb2 = wu.deg2rad(175)
P1 = ell.ell2cart(wu.deg2rad(60), wu.deg2rad(0))
P2 = ell.ell2cart(wu.deg2rad(60), wu.deg2rad(175))
para1 = ell.cart2para(P1)
para2 = ell.cart2para(P2)
cart1 = ell.para2cart(para1[0], para1[1])
cart2 = ell.para2cart(para2[0], para2[1])
ell11 = ell.cart2ell(P1)
ell21 = ell.cart2ell(P2)
ell1 = ell.cart2ell(cart1)
ell2 = ell.cart2ell(cart2)
beta0, lamb0, beta1, lamb1, c, alpha0, alpha1, s = nep.get_example(table=1, example=5)
P0 = ell.ell2cart(beta0, lamb0)
P1 = ell.ell2cart(beta1, lamb1)
c = 0.06207487624
alpha0 = wu.gms2rad([2, 52, 26.2393])
alpha1 = wu.gms2rad([177, 4, 13.6373])
s = 6705715.1610
pass
P2_num = gha1_num(ell, P1, alpha0, s, 1000)
P2_ana = gha1_ana(ell, P1, alpha0, s, 70)
# P1_num = gha1_num(ell, P0, alpha0, s, 1000)
P1_num = gha1_num(ell, P0, alpha0, s, 10000)
P1_ana = gha1_ana(ell, P0, alpha0, s, 30)
pass